The Truth about Orders of Magnitude (100th video) - YouTube

So, what are you going to do for the 100th video?

I don't know. Any good ideas in the comments?

A couple people want a Great Scientists list.

Done!

This guy Cameron wants to see a Top 10 Tops of Tents list.

Done!

Hey! It looks like you passed 10,000 subscribers too.

I’ve got it!

Hey Crazies.

How many of you have heard of an order of magnitude?

There is a nice simple way to get what we call “ballpark estimates,”

which is a baseball reference from the 1960s.

Actually, there is evidence of its use as early as 1945.

It just wasn’t in wide-spread use until the 1960s.

Whatever!

Metaphorically speaking, you don’t need to know exactly where the baseball ended up.

Sometimes you only need to know if it’s in the ballpark or outside it.

What does this have to do with the 100th video?

Everything!

No no no, don’t leave.

It'll be okay. Come back.

Let’s start with some very basic stuff.

Our decimal number system is based on 10s.

Probably because we have 10 digits on our hands.

I mean “decimal” literally means “of tens.”

Mathematically, it just means we have 10 single-digit numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

Everybody still with me? OK good.

Once we get to 10, we have to add an extra digit

and that extra digit has to count through our single-digit numbers.

We don’t get to add a third digit until 100.

In other words, we have a 1s place, and a 10s place, and 100s place,

and a 1000s place, and so on.

They’re like milestones for a decimal number system.

You know, those signs on roads that mark distance.

I seem to be using a lot of metaphors in this video.

Anyway, all those number places are powers of 10.

10 to the zero, and 10 to the 1, and 10 to the 2, and 10 to the 3, and so on;

and the power number is called an order of magnitude.

This is the 100th video on this channel, which is order of magnitude 2.

This channel also just hit 10,000 subscribers, which is order of magnitude 4.

Two different orders of magnitude at the same time!

Are you just going to geek out about numbers for 5 minutes?

OK OK, I’ll get to the point.

As it turns out, we can say every number has an order of magnitude.

Think of it like extreme rounding.

It’s whatever power of 10 is closest to that number.

But the word “closest” doesn’t always mean what you think it means.

With normal rounding, 5 is the halfway marker.

Anything from, say, 1.0 to just under 1.5 rounds down to 1

and anything from say 1.5 to 2.0 rounds up to 2.

So you would expect orders of magnitude to work the same way.

Anything from 1 to 5 rounds down to 1 and anything from 5 to 10 rounds up to 10.

But you’d be wrong!

OK, now prepare yourselves for the next bit.

We’re going to use something you probably thought you’d never see again.

Logs.

No no, logs as in logarithms.

Open your mind.

To find an order of magnitude, you first take the common log of the number.

That’s the log base 10 because we’re looking for powers of 10.

Then you round the result like normal.

But this makes orders of magnitude a little weird.

Rounding like this moves the halfway marker from half of 10 down to root 10,

or from 5 down to a little over 3, which skews toward rounding up.

By that reasoning, my height is 10 feet or 1 meter.

My weight is 100 pounds.

My mass is 100 kg.

My age is 100 years.

There are 10 billion people living on the planet.

Our next subscriber goal is 100,000; which, by orders of magnitude,

we technically achieve at 31,623.

It’s crazy, but it gives us really easy numbers to work with.

Let’s say we wanted to estimate how much it would cost to upgrade all U.S. homes to

be energy efficient.

The 2010 Census says there were about 309 million people living in the U.S.

3.09 is just shy of root 10, so we round down to 100 million.

There is an average of 2.6 people per household, which rounds down to 1.

Only 65% of homes are owned, which rounds up to 100% or 1.

So, there are 100 million owned homes in the U.S.

By orders of magnitude, energy-efficient upgrades cost $10,000.

100 million times 1 times 1 times $10,000 is $1 trillion

and, for comparison, that’s the same order of magnitude as the

2008 bank bailout.

Usually, any rounding up of one number is balanced by rounding down another,

so you can get pretty close estimates really fast.

Physicist Enrico Fermi was known for being impressively good at this.

During the first atomic bomb test, he estimated the blast yield to the correct order of magnitude

using ripped up pieces of paper.

Whoa, that guy was a genius.

Please share your thoughts in the comments and, if you’re up to the challenge,

Come up with some of your own order of magnitude estimates.

A huge thank you to all 10,000 subscribers for riding this crazy train with me.

All aboard! Ha! Ha! Ha!

A special thanks goes out to Patreon patrons like Nikko Lai,

who help make these videos better.

And until next time, remember, it’s OK to be a little crazy.

In the last video, we learned the truth behind E equals mc squared.

Comment response time!

Alright, after a bunch of your comments, I realize I could have been a bit clearer.

The title of the video was “Why Doesn’t Light Have Mass?”

The answer is that it actually might have it,

depending on how you define mass.

When most people hear the word “mass” they think of rest mass,

which light definitely doesn’t have.

However, if you’re an experimentalist, then you only care about what you can measure.

In that case, light does have mass, in every measurable way.

Light can add to something’s gravity and light can give things momentum when it

hits them.

Because it has that silly thing called “relativistic mass.”

Rest Mass + Kinetic Mass = Relativistic Mass None of our measuring devices distinguish

between different types of mass.

To them, mass is just mass.

Anyway, I apologize for the lack of clarity at the end of the video.

Totally my fault.

Hindsight is a [BEEP]!

Several of you also pointed out that light slows down in materials.

Except you’re wrong!

Well, again, this depends on your scientific philosophy.

Say you’ve got two lasers, but only one passes through a block of glass.

That one is definitely going to take longer to travel the length of the block.

So an experimentalist would say the light is going slower.

But a theoretical physicist, like myself, looks much deeper.

A lot is going on with that light inside the block.

Along the way, the photons of light have to interact with atoms.

The light in the block only appears to slow down.

It doesn’t actually slow down.

Thanks again to all 10,000 subs and to everyone who comments.

There are so many comments it’s getting very difficult to answer them all,

so, to those of you who answer each other's questions, thank you so much.

Hopefully, we can keep this up.

I’ll see you next time.

Aye! Aye! Aye!